Answer:
The region represented by the equation is a full sphere of radius √3 centered in the origin of coordinates.
Step-by-step explanation:
<em>In a plane xy, the equation that represents a circle with center in the origin, of radius r is</em>
![x^2+y^2=r^2](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3Dr%5E2)
<em>in R³, or a space xyz, we can represent a sphere with its center in the origin, and of radius r, with the equation</em>
![x^2+y^2+z^2=r^2](https://tex.z-dn.net/?f=x%5E2%2By%5E2%2Bz%5E2%3Dr%5E2)
So, in this problem we have that
![3=r^2](https://tex.z-dn.net/?f=3%3Dr%5E2)
which means that the sphere has a radius of √3.
<u>Finally, our equation is an inequality</u>, and the sphere is equal to, and less than, the calculated radius.
Therefore, the sphere is "full" from the surface to its center.
Distributing, you get
![9(2)-9(9x^{2})=18-81x^{2}](https://tex.z-dn.net/?f=9%282%29-9%289x%5E%7B2%7D%29%3D18-81x%5E%7B2%7D)
Remember that you have the
instead of
because you have a negative in front of the ![9x^{2}](https://tex.z-dn.net/?f=9x%5E%7B2%7D)
Answer:
The probability that one of the factory's bikes passed inspection and came off assembly line B is 0.564.
Step-by-step explanation:
Given : A bicycle factory runs two assembly lines, A and B. 97% of line A's products pass inspection and 94% of line B's products pass inspection. 40% of the factory's bikes come off assembly line B and the rest come off line A.
To find : The probability that one of the factory's bikes passed inspection and came off assembly line B ?
Solution :
The probability of line B's is P(B)= 40%=0.4
The probability of line A's is P(A)=100-40= 60%=0.6
Let E be the passes inspection.
The probability of line A's products pass inspection is P(E/A)=97%=0.97
The probability of line B's products pass inspection is P(E/B)=94%=0.94
The probability that one of the factory's bikes passed inspection and came off assembly line B is ![P(B\cap E)](https://tex.z-dn.net/?f=P%28B%5Ccap%20E%29)
![P(B\cap E)=P(B)\cdot P(E/B)](https://tex.z-dn.net/?f=P%28B%5Ccap%20E%29%3DP%28B%29%5Ccdot%20P%28E%2FB%29)
![P(B\cap E)=(0.6)(0.94)](https://tex.z-dn.net/?f=P%28B%5Ccap%20E%29%3D%280.6%29%280.94%29)
![P(B\cap E)=0.564](https://tex.z-dn.net/?f=P%28B%5Ccap%20E%29%3D0.564)
Therefore, The probability that one of the factory's bikes passed inspection and came off assembly line B is 0.564.
Answer:
=HI .7.5 units
Step-by-step explanation: